ACOUSTIC DISTANCE MEASUREMENT BASED ON THE INTERFERENCE BETWEEN TRANSMITTED AND REFLECTED WAVES USING CROSS-SPECTRAL METHOD BY INTRODUCING ANALYTIC SIGNAL OF LINEAR CHIRP AND HILBERT TRANSFORM FILTER

摘要

The distance to a target is fundamental information in many engineering applications. Recently, an acoustic distance measurement (ADM) method has been proposed based on the interference between transmitted and reflected waves, but it requires applying twice the Fourier transform. The ADM method in which a linear chirp whose frequency changes linearly with lapse of time is adopted as a transmitted sound has been proposed to reduce the number of applications of the Fourier transform to once. The observed wave obtained by the linear chirp signal has the distance information as a periodicity in time domain. However, due to the influence of the transfer characteristic of measuring system including a loudspeaker and microphone, the ADM method would often estimate the spurious short distance different from true distance. The ADM method by applying the cross-spectral method to observed signals of the adjacent two-channel (2ch) microphones has been also proposed, where the method adopts a linear chirp as transmitted wave and removes the influence of the measuring system. In this method, Hilbert transform is used to obtain analytic signal of linear chirp for the cross-spectrum, but Hilbert transform originally requires applying twice the Fourier transform. This paper describes an advanced study on the ADM method by applying the cross-spectral method to observed signals of the adjacent 2ch microphones, adopting a linear chirp as transmitted wave and removing the influence of the measuring system. More concretely, though the linear chirp signal in a time domain corresponds to the frequency spectrum, it is not a complex signal but a real signal. To apply the cross-spectral method, the analytic signal of linear chirp that is newly obtained using Hilbert transform filter is introduced. We confirmed the validity of the chirp-based ADM method by performing a computer simulation and by applying it to an actual sound field.